d0c02888-49fa-4e44-9297-e937796338b6 11 Валерий Очков Alvaro Diaz Falconi 4 5 false false 0 0 decimal

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Euler spiral (clothoid) and its curvature

Δt 0.00001 :

t x π 2 / sqrt 2 π / sqrt t * FresnelC * :

t y π 2 / sqrt 2 π / sqrt t * FresnelS * :

t x' t Δt + x t x - Δt / :

t y' t Δt + y t y - Δt / :

t x'' t Δt + x' t x' - Δt / :

t y'' t Δt + y' t y' - Δt / :

t κ t y'' t x' * t y' t x'' * - abs t x' (2^t y' (2^+ (3^sqrt / :

T 06 0.01 range :

T x vectorize T y vectorize augment T T κ vectorize augment